


A Penalty for Profusion

by Bitenomnom



Series: Mathematical Proof [5]
Category: Sherlock (TV)
Genre: (but I would), Fluff, Friendship, Friendship/Love, Gen, Holding Hands, M/M, Mathematics, really doesn't have to be read as Johnlock
Language: English
Status: Completed
Published: 2012-09-11
Updated: 2012-09-11
Packaged: 2017-11-14 00:41:49
Rating: Not Rated
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 1,853
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/509493
Author URL: https://archiveofourown.org/users/Bitenomnom/pseuds/Bitenomnom
Summary: <blockquote class="userstuff">
              <p>"Did you really think I was born <i>knowing</i> how to identify a zoologist by her fingernails and cutlery?"</p><p>"No, of course not." John considered turning away for the imminent lecture.</p><p>"I practiced," Sherlock reiterated instead. "Of <i>course</i> I didn’t always immediately know what to look for."</p>
            </blockquote>





	A Penalty for Profusion

**Author's Note:**

> The second week of the drabbling begins! I have to say that I'm really kind of overwhelmed by all the kudos and comments and everything you guys have been leaving on this series. (I'm a little bit embarrassed that my silly little seat-of-the-pants math drabbles are getting more attention than my bigger multi-chapter fic, but I am very happy that you like them all the same, and trust me when I say my day is made every time I see I've gotten a comment. It's really helped me get enthusiastic about this project.)
> 
> As I said in the tags, you don't necessarily have to read this as Johnlock, though of course that was where my mind was as I wrote it. It's nice as a general friendship story, too, I think. :)

**Adjusted R Squared**

When calculating an R2 value (how well a regression line fits the data points, in a range from 0, a bad fit, to 1, a perfect fit) for a linear model, adding more variables always increases R2. However, that means that your model benefits even from adding data that is not truly significant. Therefore, an “adjusted” R2 can be calculated using

1 – (1 – R2)(n-1/n-k-1)

where n is the number of observations and k is the number of independent values. This adjusted R2 imposes a penalty for including more variables, thereby discouraging the inclusion of data that is not significant simply because it will always improve (or, at worst, maintain) the R2 value.

***  
  
            

“You know my methods.”  


            John did not know Sherlock’s methods. Well—of _course_ he knew Sherlock’s methods, maybe a little better than most other people—but knowing them was very different from being able to employ them, something of which Sherlock was obviously perfectly aware but generally refused to acknowledge when he tried to goad John into deducing something (for kicks, apparently, John thought; he didn’t _really_ need John’s help).

            John wondered how it was that Sherlock started to be able to identify what pieces of evidence were important on the spot, anyway. He hardly ever brought evidence back to the flat—he wasn’t strictly allowed to, after all. “How do you know what’s important? I mean, straight away, just by glancing at it?” he asked, rather than attempting to analyze the stale pastry and accompanying butter knife in the victim’s kitchen as Sherlock had requested.

            Sherlock obviously had some sort of a smartarse comment prepared; John wasn’t sure if he should be pleased or alarmed that he could identify the exact degree to which Sherlock’s eyelids lowered just before he spat out insults to someone’s intelligence. John must have winced at the inevitable onslaught of ranting about obviousness and _don’t you see_ and _do you keep anything in that brain of yours?_ because Sherlock paused mid-eyeroll and tilted his head slightly. John supposed that even after being bombarded with John’s usual _ooh_ ing and _ahh_ ing over Sherlock’s deductions, Sherlock wasn’t used to the idea of someone taking an interest in how he’d _developed_ his methods. His eyes flashed—or glimmered, maybe. The corner of his mouth twitched upward. John knew he wasn’t the most promising student in the science of deduction, but at least he took enough interest to (he hoped so, it seemed so) make up for the staggering difference in the respective view counts of his and Sherlock’s blogs.

            “Practice,” Sherlock finally answered, the word falling from his mouth rather than being spat as Sherlock’s words usually were, lingering in a quiet way that only ever seemed to happen in times like this one, when it was just the two of them poking around an empty crime scene, no Yarders, no anybody. The upward quirk of Sherlock’s lips stuck. “Did you really think I was born _knowing_ how to identify a zoologist by her fingernails and cutlery?”

            “No, of course not,” John admitted, and considered turning away for the imminent lecture.

            “I practiced,” Sherlock reiterated instead. “Of _course_ I didn’t always immediately know what to look for.” He picked up the butter knife and sniffed it. “I solved a number of private cases on my own before I began consulting, many of them before I left for university. It was well before I had honed this particular skill.”

            John waited, silent, and took the knife when Sherlock offered it. As he glanced over the simple pattern adorning the handle for whatever it was Sherlock had seen in it, Sherlock continued. “One of them involved, appropriately, a kleptomaniac—although with the unusual twist that that in and of itself was only obliquely of relevance to the case at hand.”

            “‘Appropriately’ a kleptomaniac?”

            Sherlock took the knife back and replaced it where it had been sitting. “Before I could—as you said—tell what was important ‘straight away’—I kept a great deal of it for later study, so that I wouldn’t have to repeatedly return to the crime scene. Of course I took note of the items’ location in relation to one another and the rest of the scene first…”

            “So you just had piles of other peoples’ things in your room?” John directed his gaze to the pastry when he smiled, lest Sherlock feel self-conscious about it. John could tell from the way he stood on the balls of his feet and shifted his weight that this was, for whatever reason, a sensitive subject for Sherlock, and so he had to tread carefully.

            “I put them back when I’d solved the case, of course. I hardly needed the sort of rubbish that generally constitutes evidence,” he shrugged toward the half-eaten pastry as an example.

            Now John did look at Sherlock. “What else?”

            “Hm?” Sherlock’s tone was an absent one, and he was suddenly pulling the kitchen table to the right and staring intently at the marks left on the floor.

            “There’s something else.”

            “You think so?”

            “I’m not _that_ unobservant, Sherlock,” John crossed his arms and crouched down to look at the marks and a stray catnip mouse beneath the table.

            “Yes—well. Mycroft was frequently displeased by the state of my things.” He turned to John. “I may have placed a few in his room when mine ran out of space.”

            “In his room, huh? You put a cat liver or something under his pillow, didn’t you?”

            “Six used toothbrushes.”

            “Beside his toothbrush, I’d bet.” John couldn’t suppress a smirk.

            “Exactly.”

            “What did he do?”

            Sherlock was distracted again, replacing the table and checking through the cabinets—for something specific, by the way he quickly swung each one open and then shut with only a brief glance in-between.

            “Sherlock?”

            “Give me a moment, John,” he huffed, leaning into the sink to look down the drain and then standing back up so quickly that he smacked his head on the faucet.

            John shifted his weight from one foot to the other—he wanted to be useful, but hadn’t the slightest idea of where to look, and wasn’t particularly inclined to think about it when Sherlock was acting so oddly, so clearly flustered. “Sherlock,” he said again. “What did he do?”

            This time, Sherlock paused. He set down the cheese grater. “He threw everything out.”

            “Guess that saved you the trouble.”

            “I wasn’t done.” Sherlock turned to face John. “Whoever broke into that woman’s house and assaulted her, he was never caught.” Sherlock glanced away, holding his head at an angle that he must have believed would minimize the visibility of his sobered features from where John was standing. _This,_ this was why John always had to fight back the urge to throttle anyone who called Sherlock a sociopath (including, he thought, Sherlock himself, although Sherlock must have chosen to use the term intentionally rather than out of sheer ignorance of himself, surely). John could see Sherlock’s mouth quiver slightly.

            “Was she a friend of yours?”

            “An acquaintance,” he said, which John doubted was a sufficient explanation. He turned and took a step back to lean against the counter beside Sherlock and then reached up to pat his right shoulder. Sherlock, to his knowledge, was not generally particularly keen on physical contact, especially if it was initiated by someone else, but it seemed appropriate, and Sherlock neither shrugged him away nor spoke up in protest, so John allowed his hand to rest there. “Of course,” Sherlock said after a time, “if I would have just left it all be, it wouldn’t have been a problem.”

            “You couldn’t have known,” John said, and he squeezed a little.

            “I knew what a codger Mycroft was—is—and I provoked him all the same.”

            “Yeah, well,” John breathed, “who could blame you?” A ghost of a smile passed over Sherlock’s features. “Anyway, for someone who claims to be smarter than everybody else, I’d say that’s a pretty bloody stupid thing for him to’ve done.”

            “I’m sure he decided it was for my own good.”

            “Yeah, I’m sure,” John growled. “ _Brother knows best_.” Sherlock leaned his weight onto his left foot and John let his grip on Sherlock’s shoulder loosen, allowing his hand to follow a natural path back to his side, but Sherlock caught it before it got there. He held John’s hand against his forearm and then pulled his arm up until his fingers threaded through John’s. Sherlock’s gaze was very determinedly directed at the table, and so John pinned his eyes there as well, trying to let the waves of questions roll off his back. This was Sherlock, and if there was one thing not to overanalyze in Sherlock’s presence it was the rare gift of Sherlock’s bizarre brand of physical affection. John never asked what it meant; he wasn’t sure he cared to know. If it was important, Sherlock would tell him eventually. If it wasn’t—well—then all the more reason to appreciate that it happened at all.

            “The key to analyzing the evidence,” Sherlock finally said, clearly not interested in acknowledging the fact that he had subtly shifted his fingers to take John’s pulse, “isn’t that some parts might be relevant and some aren’t. Almost everything will tell us something—just a little. A clue to a clue to a clue, if you will.” John nodded. “With all the time and resources and space in the world, yes, we could use all of it, and perhaps come to a very vivid idea of what happened and how, complete with all the meaningless trivia you enjoy including in your blog entries. But we don’t generally have that luxury available to us. Instead, we must narrow it down to the best balance of as many of the most important things we reasonably have time to consider.”

            “Oh,” was all John could think to say. “Yes, that makes sense.” He nodded toward his right at the objects on the counter. “So what about the butter knife, then?”

            “Almost completely insignificant. She’s right handed and not sentimental, but wants to pretend she is. Completely irrelevant to the case.”

            “You just thought you’d make me try to deduce something about it anyway.”

            “Part of my method is sorting the significant from the insignificant, John, something you clearly failed to do. There is a cost to taking the time to try to incorporate every little thing into your deductions.”

            “I see. Well, guess that’s why you’re the genius and I’m not.”

            Sherlock finally met John’s eyes. “Don’t be so hard on yourself,” he muttered. “You aren’t so bad. Just slow.”

            _Like you were at the start—well, sort of, anyway,_ John thought. He doubted there was ever a point in time after age, oh, _two_ that Sherlock wasn’t smarter and quicker than most anybody else. But this wasn’t about that—this was about Sherlock, having waited so many years to hear that it was okay that for all his genius he had still made mistakes. “Yeah.” John squeezed Sherlock’s hand. “Okay.”


End file.
